Abstract:
This thesis is mainly focused to investigate the cosmological implications of Rastall gravity with the help of two dark energy models, i.e., new Tsallis agegraphic dark energy (NTADE) and Sharma-Mittal holographic dark energy (SMHDE) for interacting and non-interacting cases. The background of flat FLRWspace-timeisbeingconsideredtodevelopthedynamicalsystemofequations. To check the viability of these models and to distinguish between them, we develop important cosmological parameters including equation of state parameter, deceleration parameter, square speed of sound, statefinder and Om(z) diagnostic for both cases. By constraining the involved model parameters, it is observedthatequationofstateparameterforNTADEmodelliesinphantomregionforbothinteractingandnon-interactingcases. Whereasfornon-interacting SMHDE, it shows quintom as well as quintessence regions depending on the valuesofmodelparameter δ,anditindicatesonlythephantomregionforinteracting case. The ωD − ω′D pair shows freezing and thawing regions for non-interacting NTADE while only freezing region for interacting NTADE and non-interacting SMHDE. For interacting SMHDE case, it shows freezing and thawing regions as well as region transition from freezing to thawing. The statefinder pair (j,s) forNTADEandSMHDEindicatesarichbehaviorasitshowsdifferent DEeras; phantom, quintessence as well as Chaplygin gas for both cases. We conclude thatnon-interacting SMHDEismorephysicallyviablemodelthanNTAD Emodel because it approaches to ΛCDM limit and also the results for this model lie in stable region as shown by graphical analysis of the square speed of sound
